Question: Solve for $x$ and $y$ using substitution. ${-x-3y = -4}$ ${y = -3x+4}$
Answer: Since $y$ has already been solved for, substitute $-3x+4$ for $y$ in the first equation. ${-x - 3}{(-3x+4)}{= -4}$ Simplify and solve for $x$ $-x+9x - 12 = -4$ $8x-12 = -4$ $8x-12{+12} = -4{+12}$ $8x = 8$ $\dfrac{8x}{{8}} = \dfrac{8}{{8}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {y = -3x+4}\thinspace$ to find $y$ ${y = -3}{(1)}{ + 4}$ $y = -3 + 4$ $y = 1$ You can also plug ${x = 1}$ into $\thinspace {-x-3y = -4}\thinspace$ and get the same answer for $y$ : ${-}{(1)}{ - 3y = -4}$ ${y = 1}$